TY  - JOUR
ID  - 2007-34
T1  - A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem
A1  - Bulíček, Miroslav
A1  - Pražák, Dalibor
JA  - Applied Mathematics Letters
Y1  - 2009
VL  - 22
IS  - 7
SP  - 1025
EP  - 1028
SN  - 0893-9659
N1  - Preprint no. 2007-34
UR  - http://www.karlin.mff.cuni.cz/ncmm/preprints/07352123714BuPr1012.pdf
M2  - doi: 10.1016/j.aml.2009.01.027
KW  - Dimension of attractor
KW  - fractal dimension
KW  - Method of ℓ-trajectories
KW  - Nonlinear hyperbolic problem
KW  - Squeezing property
N2  - We study a semilinear hyperbolic problem, written as a second-order evolution equation in an infinite-dimensional Hilbert space. Assuming existence of the global attractor, we estimate its fractal dimension explicitly in terms of the data. Despite its elementary character, our technique gives reasonable results. Notably, we require no additional regularity, although nonlinear damping is allowed.
M1  - fjournal={Applied Mathematics Letters. An International Journal of Rapid Publication}
M1  - 
coden={AMLEEL}
M1  - 
mrclass={35B41 (34D45 34G20 35L70 37L30)}
M1  - 
mrnumber={MR2522993}
ER  -